Step 1: Convert the binary number to base 10. The binary number is $1100011_2$. To convert to base 10, multiply each digit by the corresponding power of 2 and sum the results. $1 \times 2^6 + 1 \times 2^5 + 0 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0$ $= 1 \times 64 + 1 \times 32 + 0 \times 16 + 0 \times 8 + 0 \times 4 + 1 \times 2 + 1 \times 1$ $= 64 + 32 + 0 + 0 + 0 + 2 + 1$ $= 99_{10}$ Step 2: Subtract 11 from the base 10 number. $99 - 11 = 88_{10}$ Step 3: Convert the result back to base 2. Divide 88 by successive powers of 2: $88 \div 64 = 1$ remainder $24$ $24 \div 32 = 0$ remainder $24$ $24 \div 16 = 1$ remainder $8$ $8 \div 8 = 1$ remainder $0$ $0 \div 4 = 0$ remainder $0$ $0 \div 2 = 0$ remainder $0$ $0 \div 1 = 0$ remainder $0$ Reading the remainders from top to bottom, we get $1011000_2$. Alternatively, using division: $88 \div 2 = 44$ remainder $0$ $44 \div 2 = 22$ remainder $0$ $22 \div 2 = 11$ remainder $0$ $11 \div 2 = 5$ remainder $1$ $5 \div 2 = 2$ remainder $1$ $2 \div 2 = 1$ remainder $0$ $1 \div 2 = 0$ remainder $1$ Reading the remainders from bottom to top: $1011000_2$. $$1011000_2$$ The final answer is $\boxed{1011000_2}$.